Boundary layer expansions of the steady MHD equations in a bounded domain

TL;DR

This paper studies the boundary layer expansions of steady MHD equations in a bounded domain, providing detailed solutions for different magnetic and velocity field regimes, extending previous theoretical work.

Contribution

It extends prior research by describing boundary layer solutions of the steady MHD system to any order under various magnetic field conditions.

Findings

Derived boundary layer expansions for different magnetic field regimes.

Extended the validity of boundary layer solutions to higher orders.

Provided theoretical framework for steady MHD boundary layer analysis.

Abstract

In this paper, we investigate the validity of boundary layer expansions for the MHD system in a rectangle. We describe the solution up to any order when the tangential magnetic field is much smaller or much larger than the tangential velocity field, thereby extending a previous work of S.J. Ding, Z.L. Lin and F. Xie.